The reintroduction of biallelic markers, now in the form of single-nucleotide polymorphisms (SNPs), has again raised concerns about the practicality of using markers with low heterozygosity for genomic screening for complex traits, even if thousands of such markers are available. Like the early blood group markers, tightly linked bialallelic SNPs can be combined into ?composite? markers with heterozygosity similar to that of short tandem repear polymorphisms (STRPs). The assumptions underlying the equivalence between single-locus multi-allelic and composite markers are identified and computer simulation used to determine the power of the Haseman-Elston test for linkage when not all of these assumptions hold. Although the power to detect linkage using a bilallelic marker (alone) was considerably less than that using a single-locus four-allele marker, the power to detect linkage using two- and three- locus composite markers was quite similar to that of a single-locus four allele marker. In the absence of complete information on phase, the inclusion of additional loci in the composite marker resulted in relatively little increase in power due to an increased probability of recombination within the composite marker and to the decrease in the ration of the number of distinct phase-unknown to phase known multi-locus genotypes (the ?phase ratio?).